You don't have to worry about traveling with your small children because they are fine when their parents are happy. If mum and dad love to travel even babies will be happy to do so. Besides, they can adapt to different situations better than anyone else.
The vast majority of countries commonly visited for tourism do not normally require any preventive vaccination. However, despite all the precautions that it is possible to adopt, for some destinations that present serious health risks it is advisable to proceed with vaccination to avoid consequences for travelers.